He was a leading member of the Japanese school of homotopy theory, following in the tradition of Hiroshi Toda.
[2] His proof in 1973 of Michael Barratt's conjecture (that positive-degree elements in the stable homotopy ring of spheres are nilpotent) was a major breakthrough: following Frank Adams' solution of the Hopf invariant one problem, it marked the beginning of a new global understanding of algebraic topology.
His contributions to the field were celebrated in 2003 at the NishidaFest[3] in Kinosaki, followed by a satellite conference at the Nagoya Institute of Technology; the proceedings were published in Geometry and Topology's monograph series.
In 2000 he was the leading organizer for a concentration year at the Japan–US Mathematics Institute[4] at Johns Hopkins University.
Some of his later work concerns a circle of ideas surrounding the Segal conjecture, transfer homomorphisms, and stable splittings of classifying spaces of groups.